Problem: Simplify to lowest terms. $\dfrac{90}{81}$
There are several ways to tackle this problem. What is the greatest common factor (GCD) of 90 and 81? $90 = 2\cdot3\cdot3\cdot5$ $81 = 3\cdot3\cdot3\cdot3$ $\mbox{GCD}(90, 81) = 3\cdot3 = 9$ $\dfrac{90}{81} = \dfrac{10 \cdot 9}{ 9\cdot 9}$ $\hphantom{\dfrac{90}{81}} = \dfrac{10}{9} \cdot \dfrac{9}{9}$ $\hphantom{\dfrac{90}{81}} = \dfrac{10}{9} \cdot 1$ $\hphantom{\dfrac{90}{81}} = \dfrac{10}{9}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{90}{81}= \dfrac{3\cdot30}{3\cdot27}= \dfrac{3\cdot 3\cdot10}{3\cdot 3\cdot9}= \dfrac{10}{9}$